Evaluating Large-Eddy Simulation (LES) and High-Speed Particle Image Velocimetry (PIV) with Phase-Invariant Proper Orthogonal Decomposition (POD)

Abstract

This study is part of a program to understand the stochastic variations in IC engine flows; in particular, it is a comparison of measured (PIV) and computed (LES) velocity from multiple cycles of the same motored engine. Comparison procedures included traditional RANS (Reynolds Averaged Navier-Stokes) decomposition (ensemble-averaged and RMS (Root Mean Square) velocity), phase-dependent, and phase- invariant POD. Phase-dependent POD was performed on the PIV and LES samples separately and on the combined samples, thus creating separate or a single POD mode sets, respectively. The phase- invariant POD was performed both on normalized snapshots and on snapshots where the original energy was conserved. Initial comparisons of the mass-specific kinetic energies of the ensemble average and RMS velocities revealed that the PIV and LES data sets differed significantly during most of the intake stroke. This discrepancy was quantifiedfirst by comparing the relevance indices calculated between ensemble average velocity fields and, second, using phase-dependent POD, which quantified cycle-to-cycle flow variations of the RANS average and turbulence. Phase-dependent POD was applied separately to the PIV and LES data sets during the intake stroke (76° ATDCE, After Top Dead Center Exhaust), where the intake-valve jet is strong and the PIV and LES data were earlier found to be significantly different. The cyclic variability of the LES ensemble average was estimated to be significantly higher than that of the PIV data set. POD was also applied to the combined sample of LES and PIV snapshots for quantitative comparison creating a single set of modes, so that comparison could be made with POD coefficients alone. Example comparisons were made at again for data at 76° and also 330° ATDCE, which is a viable spark timing in a fired engine. The results at 76° ATDCE were similar to those obtained with the POD analysis of the separate samples. At 330° ATDCE, the PIV ensemble average and RMS velocities showed somewhat more cyclic variability. Phase-invariant POD was applied to the combined PIV and LES velocity data from all crank angles to study the flow evolution over the crank angle range. Conclusions derived from the two different energy transformations are contrasted. When the energy of each velocity field is normalized, the phase-invariant POD results focus on differences in flow structures and their evolution. On the other hand, when the energy of each velocity field is conserved, the phase-invariant POD results also take into account differences in energy between the PIV and LES data.